Проверка гипотез для разности первого порядка
Summary Statistics for form1
|
num>65=0 |
num>65=1 |
Count |
64 |
63 |
Average |
4,68547 |
-0,129683 |
Standard deviation |
39,2037 |
54,5971 |
Coeff. of variation |
836,709% |
-42100,6% |
Minimum |
-103,06 |
-149,75 |
Maximum |
94,79 |
93,39 |
Range |
197,85 |
243,14 |
Stnd. skewness |
-1,09548 |
-2,5425 |
Stnd. kurtosis |
0,535014 |
0,929852 |
Comparison of Standard Deviations for form1
|
num>65=0 |
num>65=1 |
Standard deviation |
39,2037 |
54,5971 |
Variance |
1536,93 |
2980,84 |
Df |
63 |
62 |
Ratio of Variances = 0,515603
95,0% Confidence Intervals
Standard deviation of num>65=0: [33,3937; 47,4805]
Standard deviation of num>65=1: [46,4507; 66,2354]
Ratio of Variances: [0,312445; 0,849999]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0,515603 P-value = 0,00966402
Reject the null hypothesis for alpha = 0,05.
Comparison of Means for form1
95,0% confidence interval for mean of num>65=0: 4,68547 +/- 9,79282 [-5,10735; 14,4783]
95,0% confidence interval for mean of num>65=1: -0,129683 +/- 13,7501 [-13,8798; 13,6204]
95,0% confidence interval for the difference between the means
not assuming equal variances: 4,81515 +/- 16,7334 [-11,9183; 21,5486]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
not assuming equal variances: t = 0,570132 P-value = 0,569726
Do not reject the null hypothesis for alpha = 0,05.
Проверка гипотез для разности второго порядка
Summary Statistics for form2
|
num>65=0 |
num>65=1 |
Count |
63 |
63 |
Average |
-1,10857 |
-0,371746 |
Standard deviation |
53,8094 |
71,7066 |
Coeff. of variation |
-4853,94% |
-19289,1% |
Minimum |
-96,51 |
-157,21 |
Maximum |
120,73 |
189,9 |
Range |
217,24 |
347,11 |
Stnd. skewness |
1,22519 |
0,936084 |
Stnd. kurtosis |
-0,494935 |
0,513801 |
Comparison of Standard Deviations for form2
|
num>65=0 |
num>65=1 |
Standard deviation |
53,8094 |
71,7066 |
Variance |
2895,46 |
5141,84 |
Df |
62 |
62 |
Ratio of Variances = 0,563117
95,0% Confidence Intervals
Standard deviation of num>65=0: [45,7806; 65,2799]
Standard deviation of num>65=1: [61,0073; 86,9922]
Ratio of Variances: [0,340716; 0,930688]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0,563117 P-value = 0,0253078
Reject the null hypothesis for alpha = 0,05.
Comparison of Means for form2
95,0% confidence interval for mean of num>65=0: -1,10857 +/- 13,5518 [-14,6603; 12,4432]
95,0% confidence interval for mean of num>65=1: -0,371746 +/- 18,0591 [-18,4309; 17,6874]
95,0% confidence interval for the difference between the means
not assuming equal variances: -0,736825 +/- 22,3732 [-23,11; 21,6363]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
not assuming equal variances: t = -0,0652349 P-value = 0,9481
Reject the null hypothesis for alpha = 0,05.
Проверка гипотез для разности третьего порядка
Summary Statistics for form3
|
num>66=0 |
num>66=1 |
Count |
63 |
62 |
Average |
0,280317 |
1,14226 |
Standard deviation |
92,8079 |
118,661 |
Coeff. of variation |
33108,2% |
10388,3% |
Minimum |
-201,98 |
-281,73 |
Maximum |
202,16 |
306,52 |
Range |
404,14 |
588,25 |
Stnd. skewness |
0,0412798 |
0,141011 |
Stnd. kurtosis |
-0,481061 |
0,567171 |
Comparison of Standard Deviations for form3
|
num>66=0 |
num>66=1 |
Standard deviation |
92,8079 |
118,661 |
Variance |
8613,31 |
14080,5 |
Df |
62 |
61 |
Ratio of Variances = 0,611719
95,0% Confidence Intervals
Standard deviation of num>66=0: [78,9601; 112,592]
Standard deviation of num>66=1: [100,834; 144,206]
Ratio of Variances: [0,369156; 1,0126]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0,611719 P-value = 0,0559115
Do not reject the null hypothesis for alpha = 0,05.
Comparison of Means for form3
95,0% confidence interval for mean of num>66=0: 0,280317 +/- 23,3734 [-23,0931; 23,6537]
95,0% confidence interval for mean of num>66=1: 1,14226 +/- 30,1344 [-28,9921; 31,2766]
95,0% confidence interval for the difference between the means
assuming equal variances: -0,861941 +/- 37,6829 [-38,5449; 36,821]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
assuming equal variances: t = -0,0452768 P-value = 0,96396
Do not reject the null hypothesis for alpha = 0,05.
Проверка гипотез для разности четвертого порядка
Summary Statistics for form4
|
num>66=0 |
num>66=1 |
Count |
62 |
62 |
Average |
-3,35161 |
1,26855 |
Standard deviation |
170,585 |
207,603 |
Coeff. of variation |
-5089,65% |
16365,4% |
Minimum |
-392,46 |
-543,34 |
Maximum |
374,94 |
427,85 |
Range |
767,4 |
971,19 |
Stnd. skewness |
-0,271673 |
-0,301083 |
Stnd. kurtosis |
-0,476347 |
0,085268 |
Comparison of Standard Deviations for form4
|
num>66=0 |
num>66=1 |
Standard deviation |
170,585 |
207,603 |
Variance |
29099,3 |
43099,1 |
Df |
61 |
61 |
Ratio of Variances = 0,675173
95,0% Confidence Intervals
Standard deviation of num>66=0: [144,957; 207,307]
Standard deviation of num>66=1: [176,413; 252,294]
Ratio of Variances: [0,406813; 1,12056]
F-test to Compare Standard Deviations
Null hypothesis: sigma1 = sigma2
Alt. hypothesis: sigma1 NE sigma2
F = 0,675173 P-value = 0,127819
Do not reject the null hypothesis for alpha = 0,05.
Comparison of Means for form4
95,0% confidence interval for mean of num>66=0: -3,35161 +/- 43,3206 [-46,6722; 39,969]
95,0% confidence interval for mean of num>66=1: 1,26855 +/- 52,7214 [-51,4529; 53,99]
95,0% confidence interval for the difference between the means
assuming equal variances: -4,62016 +/- 67,5532 [-72,1734; 62,9331]
t test to compare means
Null hypothesis: mean1 = mean2
Alt. hypothesis: mean1 NE mean2
assuming equal variances: t = -0,135391 P-value = 0,892526
Do not reject the null hypothesis for alpha = 0,05.
Приложение 14
Построение модели типа ARIMA.
ARIMA(4,3,1)
Forecasting - ConsGOODS
Data variable: ConsGOODS
Number of observations = 129
Start index = 1.50
Sampling interval = 1,0 month(s)
Forecast Summary
Nonseasonal differencing of order: 3
Forecast model selected: ARIMA(4,3,1)
Number of forecasts generated: 1
Number of periods withheld for validation: 1
|
Estimation |
Validation |
Statistic |
Period |
Period |
RMSE |
49,7634 |
35,4549 |
MAE |
38,0752 |
35,4549 |
MAPE |
4,01628 |
3,3589 |
ME |
5,22155 |
-35,4549 |
MPE |
0,624167 |
-3,3589 |
ARIMA Model Summary
Parameter |
Estimate |
Stnd. Error |
t |
P-value |
AR(1) |
-0,772509 |
0,0882737 |
-8,75129 |
0,000000 |
AR(2) |
-0,700371 |
0,102481 |
-6,83415 |
0,000000 |
AR(3) |
-0,526385 |
0,096931 |
-5,43051 |
0,000001 |
AR(4) |
-0,263229 |
0,077883 |
-3,37979 |
0,000977 |
MA(1) |
0,988729 |
0,00549178 |
180,038 |
0,000000 |
Backforecasting: yes
Estimated white noise variance = 2494,25 with 121 degrees of freedom
Estimated white noise standard deviation = 49,9425
Number of iterations: 10
Forecast Table for ConsGOODS
Model: ARIMA(4,3,1)
V = withheld for validation
Period |
Data |
Forecast |
Residual |
|
1.50 |
813,17 |
|
|
|
2.50 |
877,02 |
|
|
|
3.50 |
844,36 |
|
|
|
4.50 |
856,69 |
863,788 |
-7,09819 |
|
5.50 |
924,97 |
885,396 |
39,5743 |
|
6.50 |
953,18 |
956,914 |
-3,73364 |
|
7.50 |
892,74 |
964,292 |
-71,5525 |
|
8.50 |
874,46 |
876,158 |
-1,69815 |
|
9.50 |
771,4 |
880,65 |
-109,25 |
|
10.50 |
785,72 |
748,872 |
36,8479 |
|
11.50 |
829,36 |
757,653 |
71,7067 |
|
12.50 |
865,08 |
790,248 |
74,832 |
|
1.51 |
892,15 |
836,335 |
55,8155 |
|
2.51 |
947,28 |
875,169 |
72,1115 |
|
3.51 |
948,6 |
974,106 |
-25,5062 |
|
4.51 |
992,79 |
969,05 |
23,7396 |
|
5.51 |
1017,36 |
1019,9 |
-2,53969 |
|
6.51 |
997,49 |
1038,82 |
-41,3253 |
|
7.51 |
911,97 |
1007,64 |
-95,669 |
|
8.51 |
837,21 |
896,604 |
-59,3937 |
|
9.51 |
857,42 |
817,276 |
40,1442 |
|
10.51 |
798,01 |
832,038 |
-34,0279 |
|
11.51 |
859,33 |
733,88 |
125,45 |
|
12.51 |
849,27 |
820,41 |
28,8602 |
|
1.52 |
838,65 |
817,118 |
21,5325 |
|
2.52 |
824,31 |
826,515 |
-2,20525 |
|
3.52 |
820,56 |
809,657 |
10,9028 |
|
4.52 |
821,28 |
821,069 |
0,211068 |
|
5.52 |
812,44 |
803,988 |
8,45172 |
|
6.52 |
786,55 |
794,107 |
-7,55734 |
|
7.52 |
804,84 |
766,149 |
38,6909 |
|
8.52 |
834,95 |
795,996 |
38,9536 |
|
9.52 |
863,61 |
828,116 |
35,4942 |
|
10.52 |
816,88 |
858,382 |
-41,5021 |
|
11.52 |
862,39 |
803,124 |
59,2661 |
|
12.52 |
839,67 |
879,335 |
-39,6649 |
|
1.53 |
812,22 |
836,913 |
-24,6931 |
|
2.53 |
822,04 |
799,014 |
23,0258 |
|
3.53 |
823,26 |
809,789 |
13,4712 |
|
4.53 |
843,39 |
817,395 |
25,9952 |
|
5.53 |
865,42 |
828,779 |
36,6411 |
|
6.53 |
825,66 |
860,085 |
-34,4248 |
|
7.53 |
850,26 |
816,855 |
33,4054 |
|
8.53 |
828,34 |
855,058 |
-26,7181 |
|
9.53 |
783,02 |
821,624 |
-38,604 |
|
10.53 |
807,71 |
762,627 |
45,0828 |
|
11.53 |
791,73 |
794,642 |
-2,91194 |
|
12.53 |
829,32 |
775,056 |
54,2645 |
|
1.54 |
863,65 |
816,287 |
47,3625 |
|
2.54 |
878,19 |
859,462 |
18,7279 |
|
3.54 |
894,68 |
886,522 |
8,15754 |
|
4.54 |
873,43 |
904,945 |
-31,515 |
|
5.54 |
841,42 |
884,695 |
-43,275 |
|
6.54 |
923,94 |
841,3 |
82,6397 |
|
7.54 |
919,01 |
938,768 |
-19,7577 |
|
8.54 |
919,19 |
910,693 |
8,49747 |
|
9.54 |
881,18 |
912,983 |
-31,8031 |
|
10.54 |
911,06 |
878,387 |
32,6727 |
|
11.54 |
921,6 |
929,349 |
-7,74859 |
|
12.54 |
1016,39 |
911,98 |
104,41 |
|
1.55 |
1055,37 |
1028,82 |
26,5453 |
|
2.55 |
1103,51 |
1065,93 |
37,5767 |
|
3.55 |
1112,47 |
1139,99 |
-27,5241 |
|
4.55 |
1119,03 |
1147,76 |
-28,7315 |
|
5.55 |
1113,04 |
1159,71 |
-46,6693 |
|
6.55 |
1028,2 |
1131,07 |
-102,868 |
|
7.55 |
1038,78 |
1017,91 |
20,8711 |
|
8.55 |
1086,43 |
1031,61 |
54,8152 |
|
9.55 |
1105,96 |
1077,55 |
28,4141 |
|
10.55 |
1125,8 |
1086,22 |
39,5784 |
|
11.55 |
1124,88 |
1115,35 |
9,52579 |
|
12.55 |
1162,68 |
1139,82 |
22,8588 |
|
1.56 |
1204,92 |
1187,6 |
17,3184 |
|
2.56 |
1232,24 |
1222,91 |
9,33235 |
|
3.56 |
1138,69 |
1248,61 |
-109,924 |
|
4.56 |
1230,79 |
1130,75 |
100,041 |
|
5.56 |
1271,72 |
1266,26 |
5,46391 |
|
6.56 |
1307,78 |
1285,21 |
22,5679 |
|
7.56 |
1328,18 |
1313,29 |
14,8873 |
|
8.56 |
1310,47 |
1338,08 |
-27,6124 |
|
9.56 |
1326,15 |
1344,82 |
-18,6672 |
|
10.56 |
1344,56 |
1347,66 |
-3,09791 |
|
11.56 |
1348,83 |
1357,03 |
-8,19916 |
|
12.56 |
1324,74 |
1349,85 |
-25,1053 |
|
1.57 |
1347,72 |
1317,23 |
30,4892 |
|
2.57 |
1213,49 |
1356,26 |
-142,774 |
|
3.57 |
1145,62 |
1180,12 |
-34,4999 |
|
4.57 |
1180,98 |
1112,62 |
68,3591 |
|
5.57 |
1181,07 |
1154,59 |
26,4784 |
|
6.57 |
1145,27 |
1136,97 |
8,30172 |
|
7.57 |
995,52 |
1084,59 |
-89,0744 |
|
8.57 |
957,73 |
943,826 |
13,9042 |
|
9.57 |
1030,47 |
935,09 |
95,3805 |
|
10.57 |
987,7 |
1003,57 |
-15,8712 |
|
11.57 |
874,21 |
922,364 |
-48,1537 |
|
12.57 |
749,78 |
802,609 |
-52,829 |
|
1.58 |
815,25 |
708,454 |
106,796 |
|
2.58 |
788,89 |
803,932 |
-15,042 |
|
3.58 |
688,15 |
719,292 |
-31,1416 |
|
4.58 |
689,85 |
606,201 |
83,6491 |
|
5.58 |
758,83 |
657,899 |
100,931 |
|
6.58 |
813,63 |
763,592 |
50,0378 |
|
7.58 |
820,49 |
794,661 |
25,829 |
|
8.58 |
906,61 |
808,968 |
97,6421 |
|
9.58 |
902,04 |
952,964 |
-50,9242 |
|
10.58 |
941,57 |
938,544 |
3,02568 |
|
11.58 |
988,37 |
979,04 |
9,32958 |
|
12.58 |
1024,29 |
1023,24 |
1,04948 |
|
1.59 |
1117,68 |
1061,89 |
55,7877 |
|
2.59 |
1125,11 |
1157,2 |
-32,088 |
|
3.59 |
1142,6 |
1160,49 |
-17,8856 |
|
4.59 |
1196,45 |
1182,91 |
13,5389 |
|
5.59 |
1193,84 |
1243,21 |
-49,3748 |
|
6.59 |
1163,26 |
1224,08 |
-60,8242 |
|
7.59 |
1141,02 |
1168,73 |
-27,7092 |
|
8.59 |
1170,72 |
1148,45 |
22,2703 |
|
9.59 |
1132,32 |
1180,66 |
-48,345 |
|
10.59 |
1143,91 |
1109,2 |
34,7066 |
|
11.59 |
1120,08 |
1131,51 |
-11,4334 |
|
12.59 |
1128,26 |
1107,12 |
21,1418 |
|
1.60 |
1207,35 |
1124,71 |
82,638 |
|
2.60 |
1148,54 |
1212,24 |
-63,7007 |
|
3.60 |
1163,89 |
1135,86 |
28,0259 |
|
4.60 |
1166,96 |
1169,89 |
-2,93031 |
|
5.60 |
1156,66 |
1178,58 |
-21,9171 |
|
6.60 |
1155,66 |
1159,38 |
-3,72177 |
|
7.60 |
1134,28 |
1140,57 |
-6,29092 |
|
8.60 |
1104,87 |
1129,12 |
-24,2479 |
|
9.60 |
1055,55 |
1091,0 |
-35,4549 |
V |
|
|
Lower 95,0% |
Upper 95,0% |
Period |
Forecast |
Limit |
Limit |
10.60 |
1031,56 |
932,684 |
1130,43 |
ARIMA(3,3,1)
Forecasting - ConsGOODS
Data variable: ConsGOODS
Number of observations = 129
Start index = 1.50
Sampling interval = 1,0 month(s)
Forecast Summary
Nonseasonal differencing of order: 3
Forecast model selected: ARIMA(3,3,1)
Number of forecasts generated: 1
Number of periods withheld for validation: 1
|
Estimation |
Validation |
Statistic |
Period |
Period |
RMSE |
53,84 |
16,6713 |
MAE |
41,849 |
16,6713 |
MAPE |
4,39063 |
1,5794 |
ME |
18,0535 |
-16,6713 |
MPE |
1,92528 |
-1,5794 |
ARIMA Model Summary
Parameter |
Estimate |
Stnd. Error |
t |
P-value |
AR(1) |
-0,691033 |
0,0855976 |
-8,07304 |
0,000000 |
AR(2) |
-0,545163 |
0,0766751 |
-7,11004 |
0,000000 |
AR(3) |
-0,325177 |
0,0762359 |
-4,2654 |
0,000040 |
MA(1) |
0,998004 |
0,00166574 |
599,134 |
0,000000 |
Backforecasting: yes
Estimated white noise variance = 2621,47 with 122 degrees of freedom
Estimated white noise standard deviation = 51,2003
Number of iterations: 13
Forecast Table for ConsGOODS
Model: ARIMA(3,3,1)
V = withheld for validation
Period |
Data |
Forecast |
Residual |
|
1.50 |
813,17 |
|
|
|
2.50 |
877,02 |
|
|
|
3.50 |
844,36 |
|
|
|
4.50 |
856,69 |
862,796 |
-6,10614 |
|
5.50 |
924,97 |
874,361 |
50,6091 |
|
6.50 |
953,18 |
940,153 |
13,0274 |
|
7.50 |
892,74 |
942,684 |
-49,9441 |
|
8.50 |
874,46 |
875,847 |
-1,38742 |
|
9.50 |
771,4 |
867,038 |
-95,6381 |
|
10.50 |
785,72 |
711,211 |
74,5088 |
|
11.50 |
829,36 |
730,027 |
99,3327 |
|
12.50 |
865,08 |
795,106 |
69,9742 |
|
1.51 |
892,15 |
831,049 |
61,1011 |
|
2.51 |
947,28 |
899,032 |
48,2478 |
|
3.51 |
948,6 |
969,458 |
-20,8583 |
|
4.51 |
992,79 |
953,726 |
39,064 |
|
5.51 |
1017,36 |
1006,75 |
10,6099 |
|
6.51 |
997,49 |
1028,82 |
-31,3298 |
|
7.51 |
911,97 |
984,228 |
-72,2579 |
|
8.51 |
837,21 |
881,422 |
-44,2117 |
|
9.51 |
857,42 |
784,165 |
73,2547 |
|
10.51 |
798,01 |
806,541 |
-8,53077 |
|
11.51 |
859,33 |
717,386 |
141,944 |
|
12.51 |
849,27 |
829,068 |
20,202 |
|
1.52 |
838,65 |
827,972 |
10,6781 |
|
2.52 |
824,31 |
807,456 |
16,8536 |
|
3.52 |
820,56 |
815,475 |
5,08504 |
|
4.52 |
821,28 |
791,13 |
30,1499 |
|
5.52 |
812,44 |
793,836 |
18,6043 |
|
6.52 |
786,55 |
783,851 |
2,69883 |
|
7.52 |
804,84 |
755,731 |
49,1089 |
|
8.52 |
834,95 |
784,633 |
50,3173 |
|
9.52 |
863,61 |
818,08 |
45,5298 |
|
10.52 |
816,88 |
852,282 |
-35,402 |
|
11.52 |
862,39 |
798,943 |
63,4466 |
|
12.52 |
839,67 |
865,607 |
-25,9366 |
|
1.53 |
812,22 |
818,153 |
-5,93279 |
|
2.53 |
822,04 |
775,053 |
46,9867 |
|
3.53 |
823,26 |
810,777 |
12,4831 |
|
4.53 |
843,39 |
791,574 |
51,816 |
|
5.53 |
865,42 |
823,056 |
42,3637 |
|
6.53 |
825,66 |
858,744 |
-33,0838 |
|
7.53 |
850,26 |
801,467 |
48,7928 |
|
8.53 |
828,34 |
843,603 |
-15,2635 |
|
9.53 |
783,02 |
803,693 |
-20,673 |
|
10.53 |
807,71 |
738,382 |
69,3284 |
|
11.53 |
791,73 |
792,122 |
-0,392045 |
|
12.53 |
829,32 |
753,513 |
75,8069 |
|
1.54 |
863,65 |
809,665 |
53,9847 |
|
2.54 |
878,19 |
864,729 |
13,4611 |
|
3.54 |
894,68 |
871,266 |
23,4145 |
|
4.54 |
873,43 |
902,221 |
-28,7905 |
|
5.54 |
841,42 |
864,123 |
-22,7035 |
|
6.54 |
923,94 |
817,232 |
106,708 |
|
7.54 |
919,01 |
926,113 |
-7,10348 |
|
8.54 |
919,19 |
896,217 |
22,9725 |
|
9.54 |
881,18 |
906,962 |
-25,7819 |
|
10.54 |
911,06 |
875,851 |
35,2089 |
|
11.54 |
921,6 |
893,894 |
27,7062 |
|
12.54 |
1016,39 |
901,677 |
114,713 |
|
1.55 |
1055,37 |
1022,42 |
32,9481 |
|
2.55 |
1103,51 |
1074,34 |
29,1745 |
|
3.55 |
1112,47 |
1129,47 |
-16,9978 |
|
4.55 |
1119,03 |
1142,74 |
-23,7134 |
|
5.55 |
1113,04 |
1126,67 |
-13,6263 |
|
6.55 |
1028,2 |
1110,78 |
-82,581 |
|
7.55 |
1038,78 |
986,315 |
52,4649 |
|
8.55 |
1086,43 |
1011,44 |
74,9917 |
|
9.55 |
1105,96 |
1063,18 |
42,7766 |
|
10.55 |
1125,8 |
1074,87 |
50,931 |
|
11.55 |
1124,88 |
1129,99 |
-5,10785 |
|
12.55 |
1162,68 |
1128,56 |
34,123 |
|
1.56 |
1204,92 |
1166,28 |
38,6357 |
|
2.56 |
1232,24 |
1211,16 |
21,0848 |
|
3.56 |
1138,69 |
1236,32 |
-97,6324 |
|
4.56 |
1230,79 |
1116,62 |
114,166 |
|
5.56 |
1271,72 |
1246,84 |
24,8783 |
|
6.56 |
1307,78 |
1267,65 |
40,129 |
|
7.56 |
1328,18 |
1296,36 |
31,8214 |
|
8.56 |
1310,47 |
1360,39 |
-49,9156 |
|
9.56 |
1326,15 |
1310,81 |
15,3437 |
|
10.56 |
1344,56 |
1326,25 |
18,3144 |
|
11.56 |
1348,83 |
1336,93 |
11,8997 |
|
12.56 |
1324,74 |
1332,21 |
-7,46639 |
|
1.57 |
1347,72 |
1308,73 |
38,9852 |
|
2.57 |
1213,49 |
1339,98 |
-126,486 |
|
3.57 |
1145,62 |
1152,95 |
-7,33007 |
|
4.57 |
1180,98 |
1083,77 |
97,211 |
|
5.57 |
1181,07 |
1141,62 |
39,4504 |
|
6.57 |
1145,27 |
1109,43 |
35,8434 |
|
7.57 |
995,52 |
1101,75 |
-106,232 |
|
8.57 |
957,73 |
937,157 |
20,5727 |
|
9.57 |
1030,47 |
898,014 |
132,456 |
|
10.57 |
987,7 |
984,762 |
2,93778 |
|
11.57 |
874,21 |
910,008 |
-35,7982 |
|
12.57 |
749,78 |
818,469 |
-68,689 |
|
1.58 |
815,25 |
690,737 |
124,513 |
|
2.58 |
788,89 |
760,414 |
28,4761 |
|
3.58 |
688,15 |
708,036 |
-19,8859 |
|
4.58 |
689,85 |
609,098 |
80,752 |
|
5.58 |
758,83 |
673,31 |
85,5204 |
|
6.58 |
813,63 |
731,967 |
81,663 |
|
7.58 |
820,49 |
790,712 |
29,7782 |
|
8.58 |
906,61 |
828,863 |
77,7473 |
|
9.58 |
902,04 |
951,392 |
-49,3521 |
|
10.58 |
941,57 |
915,108 |
26,4621 |
|
11.58 |
988,37 |
956,934 |
31,4357 |
|
12.58 |
1024,29 |
1018,3 |
5,9909 |
|
1.59 |
1117,68 |
1032,14 |
85,5389 |
|
2.59 |
1125,11 |
1157,81 |
-32,7007 |
|
3.59 |
1142,6 |
1146,97 |
-4,37039 |
|
4.59 |
1196,45 |
1164,13 |
32,3244 |
|
5.59 |
1193,84 |
1230,52 |
-36,6794 |
|
6.59 |
1163,26 |
1189,96 |
-26,6967 |
|
7.59 |
1141,02 |
1153,72 |
-12,6957 |
|
8.59 |
1170,72 |
1129,35 |
41,3698 |
|
9.59 |
1132,32 |
1151,88 |
-19,5646 |
|
10.59 |
1143,91 |
1092,72 |
51,1891 |
|
11.59 |
1120,08 |
1124,06 |
-3,9826 |
|
12.59 |
1128,26 |
1098,48 |
29,7783 |
|
1.60 |
1207,35 |
1100,3 |
107,053 |
|
2.60 |
1148,54 |
1214,64 |
-66,1025 |
|
3.60 |
1163,89 |
1118,96 |
44,9283 |
|
4.60 |
1166,96 |
1163,21 |
3,75297 |
|
5.60 |
1156,66 |
1166,03 |
-9,3703 |
|
6.60 |
1155,66 |
1121,26 |
34,3982 |
|
7.60 |
1134,28 |
1142,67 |
-8,3872 |
|
8.60 |
1104,87 |
1109,4 |
-4,52592 |
|
9.60 |
1055,55 |
1072,22 |
-16,6713 |
V |
|
|
Lower 95,0% |
Upper 95,0% |
Period |
Forecast |
Limit |
Limit |
10.60 |
1014,09 |
912,73 |
1115,44 |
ARIMA(3,4,2)
Forecasting - ConsGOODS
Data variable: ConsGOODS
Number of observations = 129
Start index = 1.50
Sampling interval = 1,0 month(s)
Forecast Summary
Nonseasonal differencing of order: 4
Forecast model selected: ARIMA(3,4,2)
Number of forecasts generated: 1
Number of periods withheld for validation: 1
|
Estimation |
Validation |
Statistic |
Period |
Period |
RMSE |
55,3315 |
24,2886 |
MAE |
41,7095 |
24,2886 |
MAPE |
4,37794 |
2,30104 |
ME |
-0,367182 |
-24,2886 |
MPE |
-0,00138258 |
-2,30104 |
ARIMA Model Summary
Parameter |
Estimate |
Stnd. Error |
t |
P-value |
AR(1) |
-0,725974 |
0,0747026 |
-9,7182 |
0,000000 |
AR(2) |
-0,565381 |
0,089226 |
-6,33651 |
0,000000 |
AR(3) |
-0,324779 |
0,0734021 |
-4,42465 |
0,000021 |
MA(1) |
1,81315 |
0,00124842 |
1452,35 |
0,000000 |
MA(2) |
-0,820672 |
0,00165549 |
-495,727 |
0,000000 |
Backforecasting: yes
Estimated white noise variance = 3115,73 with 120 degrees of freedom
Estimated white noise standard deviation = 55,8187
Number of iterations: 44
Forecast Table for ConsGOODS
Model: ARIMA(3,4,2)
V = withheld for validation
Period |
Data |
Forecast |
Residual |
|
1.50 |
813,17 |
|
|
|
2.50 |
877,02 |
|
|
|
3.50 |
844,36 |
|
|
|
4.50 |
856,69 |
|
|
|
5.50 |
924,97 |
873,225 |
51,7454 |
|
6.50 |
953,18 |
955,204 |
-2,02384 |
|
7.50 |
892,74 |
960,869 |
-68,1285 |
|
8.50 |
874,46 |
885,377 |
-10,9175 |
|
9.50 |
771,4 |
870,724 |
-99,3245 |
|
10.50 |
785,72 |
698,039 |
87,6806 |
|
11.50 |
829,36 |
727,636 |
101,724 |
|
12.50 |
865,08 |
810,112 |
54,9677 |
|
1.51 |
892,15 |
859,764 |
32,3864 |
|
2.51 |
947,28 |
935,248 |
12,0317 |
|
3.51 |
948,6 |
1007,62 |
-59,0154 |
|
4.51 |
992,79 |
984,179 |
8,61145 |
|
5.51 |
1017,36 |
1037,74 |
-20,3844 |
|
6.51 |
997,49 |
1056,96 |
-59,4739 |
|
7.51 |
911,97 |
1004,12 |
-92,1514 |
|
8.51 |
837,21 |
885,643 |
-48,4325 |
|
9.51 |
857,42 |
776,664 |
80,7556 |
|
10.51 |
798,01 |
808,613 |
-10,603 |
|
11.51 |
859,33 |
721,656 |
137,674 |
|
12.51 |
849,27 |
854,995 |
-5,72487 |
|
1.52 |
838,65 |
856,07 |
-17,4198 |
|
2.52 |
824,31 |
834,413 |
-10,1031 |
|
3.52 |
820,56 |
839,627 |
-19,0671 |
|
4.52 |
821,28 |
811,74 |
9,53968 |
|
5.52 |
812,44 |
816,387 |
-3,94682 |
|
6.52 |
786,55 |
806,614 |
-20,0645 |
|
7.52 |
804,84 |
775,62 |
29,2196 |
|
8.52 |
834,95 |
808,077 |
26,8735 |
|
9.52 |
863,61 |
846,741 |
16,8692 |
|
10.52 |
816,88 |
885,754 |
-68,8743 |
|
11.52 |
862,39 |
823,192 |
39,1985 |
|
12.52 |
839,67 |
892,902 |
-53,232 |
|
1.53 |
812,22 |
838,254 |
-26,0342 |
|
2.53 |
822,04 |
791,506 |
30,5337 |
|
3.53 |
823,26 |
829,942 |
-6,6821 |
|
4.53 |
843,39 |
810,39 |
32,9998 |
|
5.53 |
865,42 |
848,013 |
17,4067 |
|
6.53 |
825,66 |
887,232 |
-61,572 |
|
7.53 |
850,26 |
821,572 |
28,6884 |
|
8.53 |
828,34 |
865,855 |
-37,5154 |
|
9.53 |
783,02 |
820,491 |
-37,4712 |
|
10.53 |
807,71 |
749,649 |
58,0609 |
|
11.53 |
791,73 |
809,987 |
-18,2575 |
|
12.53 |
829,32 |
770,056 |
59,2643 |
|
1.54 |
863,65 |
836,075 |
27,5753 |
|
2.54 |
878,19 |
896,627 |
-18,4373 |
|
3.54 |
894,68 |
902,072 |
-7,39173 |
|
4.54 |
873,43 |
931,628 |
-58,1978 |
|
5.54 |
841,42 |
884,076 |
-42,6562 |
|
6.54 |
923,94 |
829,112 |
94,8277 |
|
7.54 |
919,01 |
950,223 |
-31,2127 |
|
8.54 |
919,19 |
919,42 |
-0,229884 |
|
9.54 |
881,18 |
931,116 |
-49,9363 |
|
10.54 |
911,06 |
890,427 |
20,6327 |
|
11.54 |
921,6 |
909,225 |
12,3752 |
|
12.54 |
1016,39 |
920,07 |
96,3197 |
|
1.55 |
1055,37 |
1056,78 |
-1,41171 |
|
2.55 |
1103,51 |
1111,87 |
-8,357 |
|
3.55 |
1112,47 |
1166,71 |
-54,2384 |
|
4.55 |
1119,03 |
1170,87 |
-51,8365 |
|
5.55 |
1113,04 |
1145,12 |
-32,0846 |
|
6.55 |
1028,2 |
1122,73 |
-94,529 |
|
7.55 |
1038,78 |
982,926 |
55,8538 |
|
8.55 |
1086,43 |
1012,54 |
73,8883 |
|
9.55 |
1105,96 |
1075,77 |
30,1946 |
|
10.55 |
1125,8 |
1096,42 |
29,3766 |
|
11.55 |
1124,88 |
1157,35 |
-32,467 |
|
12.55 |
1162,68 |
1150,33 |
12,3476 |
|
1.56 |
1204,92 |
1188,75 |
16,1695 |
|
2.56 |
1232,24 |
1236,74 |
-4,49805 |
|
3.56 |
1138,69 |
1262,72 |
-124,033 |
|
4.56 |
1230,79 |
1124,4 |
106,392 |
|
5.56 |
1271,72 |
1265,03 |
6,68818 |
|
6.56 |
1307,78 |
1289,22 |
18,5629 |
|
7.56 |
1328,18 |
1324,8 |
3,38352 |
|
8.56 |
1310,47 |
1389,07 |
-78,5995 |
|
9.56 |
1326,15 |
1326,28 |
-0,130909 |
|
10.56 |
1344,56 |
1339,38 |
5,17838 |
|
11.56 |
1348,83 |
1350,38 |
-1,54823 |
|
12.56 |
1324,74 |
1346,38 |
-21,6422 |
|
1.57 |
1347,72 |
1319,5 |
28,2211 |
|
2.57 |
1213,49 |
1353,21 |
-139,719 |
|
3.57 |
1145,62 |
1145,78 |
-0,157686 |
|
4.57 |
1180,98 |
1071,72 |
109,259 |
|
5.57 |
1181,07 |
1142,69 |
38,3785 |
|
6.57 |
1145,27 |
1121,38 |
23,8858 |
|
7.57 |
995,52 |
1120,84 |
-125,317 |
|
8.57 |
957,73 |
935,803 |
21,9271 |
|
9.57 |
1030,47 |
893,537 |
136,933 |
|
10.57 |
987,7 |
1000,36 |
-12,6589 |
|
11.57 |
874,21 |
931,582 |
-57,3716 |
|
12.57 |
749,78 |
832,635 |
-82,8547 |
|
1.58 |
815,25 |
686,279 |
128,971 |
|
2.58 |
788,89 |
770,778 |
18,1117 |
|
3.58 |
688,15 |
727,686 |
-39,5359 |
|
4.58 |
689,85 |
626,854 |
62,9957 |
|
5.58 |
758,83 |
696,022 |
62,8078 |
|
6.58 |
813,63 |
764,369 |
49,2614 |
|
7.58 |
820,49 |
836,718 |
-16,2283 |
|
8.58 |
906,61 |
875,897 |
30,7134 |
|
9.58 |
902,04 |
1001,4 |
-99,3595 |
|
10.58 |
941,57 |
951,417 |
-9,84713 |
|
11.58 |
988,37 |
990,796 |
-2,42616 |
|
12.58 |
1024,29 |
1050,73 |
-26,4431 |
|
1.59 |
1117,68 |
1061,63 |
56,0492 |
|
2.59 |
1125,11 |
1195,94 |
-70,8335 |
|
3.59 |
1142,6 |
1176,35 |
-33,7545 |
|
4.59 |
1196,45 |
1187,05 |
9,40039 |
|
5.59 |
1193,84 |
1252,23 |
-58,3903 |
|
6.59 |
1163,26 |
1203,66 |
-40,4033 |
|
7.59 |
1141,02 |
1160,46 |
-19,442 |
|
8.59 |
1170,72 |
1129,95 |
40,7724 |
|
9.59 |
1132,32 |
1156,97 |
-24,6453 |
|
10.59 |
1143,91 |
1096,06 |
47,8464 |
|
11.59 |
1120,08 |
1133,88 |
-13,7965 |
|
12.59 |
1128,26 |
1105,95 |
22,3104 |
|
1.60 |
1207,35 |
1110,86 |
96,4869 |
|
2.60 |
1148,54 |
1240,01 |
-91,4656 |
|
3.60 |
1163,89 |
1134,37 |
29,5225 |
|
4.60 |
1166,96 |
1180,64 |
-13,6837 |
|
5.60 |
1156,66 |
1179,55 |
-22,8911 |
|
6.60 |
1155,66 |
1132,29 |
23,3699 |
|
7.60 |
1134,28 |
1156,91 |
-22,6327 |
|
8.60 |
1104,87 |
1119,91 |
-15,037 |
|
9.60 |
1055,55 |
1079,84 |
-24,2886 |
V |
|
|
Lower 95,0% |
Upper 95,0% |
Period |
Forecast |
Limit |
Limit |
10.60 |
1016,97 |
906,451 |
1127,49 |
ARIMA(4,4,2)
Forecasting - ConsGOODS
Data variable: ConsGOODS
Number of observations = 129
Start index = 1.50
Sampling interval = 1,0 month(s)
Forecast Summary
Nonseasonal differencing of order: 4
Forecast model selected: ARIMA(4,4,2)
Number of forecasts generated: 1
Number of periods withheld for validation: 1
|
Estimation |
Validation |
Statistic |
Period |
Period |
RMSE |
55,4542 |
25,2777 |
MAE |
41,8945 |
25,2777 |
MAPE |
4,41688 |
2,39475 |
ME |
2,43142 |
-25,2777 |
MPE |
0,319291 |
-2,39475 |
ARIMA Model Summary
Parameter |
Estimate |
Stnd. Error |
t |
P-value |
AR(1) |
-0,892822 |
0,0882865 |
-10,1128 |
0,000000 |
AR(2) |
-0,804313 |
0,0928404 |
-8,66339 |
0,000000 |
AR(3) |
-0,66076 |
0,104261 |
-6,33758 |
0,000000 |
AR(4) |
-0,385011 |
0,0791228 |
-4,86599 |
0,000004 |
MA(1) |
1,64643 |
0,0181942 |
90,4921 |
0,000000 |
MA(2) |
-0,653774 |
0,0196479 |
-33,2745 |
0,000000 |
Backforecasting: yes
Estimated white noise variance = 3113,8 with 119 degrees of freedom
Estimated white noise standard deviation = 55,8014
Number of iterations: 14
Forecast Table for ConsGOODS
Model: ARIMA(4,4,2)
V = withheld for validation
Period |
Data |
Forecast |
Residual |
|
1.50 |
813,17 |
|
|
|
2.50 |
877,02 |
|
|
|
3.50 |
844,36 |
|
|
|
4.50 |
856,69 |
|
|
|
5.50 |
924,97 |
868,973 |
55,997 |
|
6.50 |
953,18 |
951,514 |
1,66603 |
|
7.50 |
892,74 |
959,697 |
-66,957 |
|
8.50 |
874,46 |
843,561 |
30,8989 |
|
9.50 |
771,4 |
857,13 |
-85,7299 |
|
10.50 |
785,72 |
713,65 |
72,0696 |
|
11.50 |
829,36 |
721,56 |
107,8 |
|
12.50 |
865,08 |
779,551 |
85,5293 |
|
1.51 |
892,15 |
855,134 |
37,0161 |
|
2.51 |
947,28 |
896,399 |
50,881 |
|
3.51 |
948,6 |
1022,97 |
-74,3735 |
|
4.51 |
992,79 |
1002,02 |
-9,23218 |
|
5.51 |
1017,36 |
1040,27 |
-22,9131 |
|
6.51 |
997,49 |
1053,95 |
-56,4577 |
|
7.51 |
911,97 |
1008,4 |
-96,4294 |
|
8.51 |
837,21 |
864,352 |
-27,1416 |
|
9.51 |
857,42 |
777,594 |
79,8257 |
|
10.51 |
798,01 |
805,268 |
-7,25827 |
|
11.51 |
859,33 |
707,424 |
151,906 |
|
12.51 |
849,27 |
817,544 |
31,7258 |
|
1.52 |
838,65 |
839,628 |
-0,977657 |
|
2.52 |
824,31 |
853,448 |
-29,1375 |
|
3.52 |
820,56 |
819,963 |
0,597388 |
|
4.52 |
821,28 |
842,95 |
-21,6703 |
|
5.52 |
812,44 |
808,26 |
4,17968 |
|
6.52 |
786,55 |
799,395 |
-12,8449 |
|
7.52 |
804,84 |
767,297 |
37,5429 |
|
8.52 |
834,95 |
804,808 |
30,142 |
|
9.52 |
863,61 |
846,449 |
17,1613 |
|
10.52 |
816,88 |
879,308 |
-62,4275 |
|
11.52 |
862,39 |
809,018 |
53,3721 |
|
12.52 |
839,67 |
895,621 |
-55,951 |
|
1.53 |
812,22 |
846,638 |
-34,4182 |
|
2.53 |
822,04 |
791,296 |
30,7436 |
|
3.53 |
823,26 |
800,853 |
22,407 |
|
4.53 |
843,39 |
827,295 |
16,0955 |
|
5.53 |
865,42 |
831,224 |
34,1958 |
|
6.53 |
825,66 |
873,628 |
-47,9684 |
|
7.53 |
850,26 |
824,582 |
25,6777 |
|
8.53 |
828,34 |
860,95 |
-32,6098 |
|
9.53 |
783,02 |
826,417 |
-43,3971 |
|
10.53 |
807,71 |
751,093 |
56,6174 |
|
11.53 |
791,73 |
787,227 |
4,50347 |
|
12.53 |
829,32 |
782,399 |
46,9214 |
|
1.54 |
863,65 |
823,57 |
40,0798 |
|
2.54 |
878,19 |
880,428 |
-2,23832 |
|
3.54 |
894,68 |
914,999 |
-20,3191 |
|
4.54 |
873,43 |
921,193 |
-47,7632 |
|
5.54 |
841,42 |
895,705 |
-54,2846 |
|
6.54 |
923,94 |
832,861 |
91,0793 |
|
7.54 |
919,01 |
945,294 |
-26,2837 |
|
8.54 |
919,19 |
920,19 |
-0,999786 |
|
9.54 |
881,18 |
911,13 |
-29,9501 |
|
10.54 |
911,06 |
873,13 |
37,9298 |
|
11.54 |
921,6 |
940,167 |
-18,5671 |
|
12.54 |
1016,39 |
909,75 |
106,64 |
|
1.55 |
1055,37 |
1050,02 |
5,34767 |
|
2.55 |
1103,51 |
1093,67 |
9,84029 |
|
3.55 |
1112,47 |
1174,33 |
-61,8606 |
|
4.55 |
1119,03 |
1165,98 |
-46,9463 |
|
5.55 |
1113,04 |
1170,29 |
-57,2529 |
|
6.55 |
1028,2 |
1117,29 |
-89,0896 |
|
7.55 |
1038,78 |
982,719 |
56,0606 |
|
8.55 |
1086,43 |
997,119 |
89,311 |
|
9.55 |
1105,96 |
1071,77 |
34,1884 |
|
10.55 |
1125,8 |
1090,15 |
35,6542 |
|
11.55 |
1124,88 |
1121,03 |
3,85119 |
|
12.55 |
1162,68 |
1162,07 |
0,605166 |
|
1.56 |
1204,92 |
1208,87 |
-3,95123 |
|
2.56 |
1232,24 |
1239,81 |
-7,56754 |
|
3.56 |
1138,69 |
1263,08 |
-124,392 |
|
4.56 |
1230,79 |
1114,42 |
116,366 |
|
5.56 |
1271,72 |
1269,77 |
1,94944 |
|
6.56 |
1307,78 |
1302,35 |
5,43066 |
|
7.56 |
1328,18 |
1322,64 |
5,54272 |
|
8.56 |
1310,47 |
1340,02 |
-29,5508 |
|
9.56 |
1326,15 |
1362,92 |
-36,773 |
|
10.56 |
1344,56 |
1342,16 |
2,39922 |
|
11.56 |
1348,83 |
1352,38 |
-3,54887 |
|
12.56 |
1324,74 |
1341,77 |
-17,0289 |
|
1.57 |
1347,72 |
1301,66 |
46,0592 |
|
2.57 |
1213,49 |
1354,28 |
-140,792 |
|
3.57 |
1145,62 |
1150,25 |
-4,6301 |
|
4.57 |
1180,98 |
1065,98 |
115,0 |
|
5.57 |
1181,07 |
1136,94 |
44,1264 |
|
6.57 |
1145,27 |
1141,65 |
3,62268 |
|
7.57 |
995,52 |
1072,43 |
-76,9112 |
|
8.57 |
957,73 |
928,758 |
28,9721 |
|
9.57 |
1030,47 |
927,136 |
103,334 |
|
10.57 |
987,7 |
1017,69 |
-29,9894 |
|
11.57 |
874,21 |
932,666 |
-58,4561 |
|
12.57 |
749,78 |
783,467 |
-33,6867 |
|
1.58 |
815,25 |
696,162 |
119,088 |
|
2.58 |
788,89 |
822,892 |
-34,002 |
|
3.58 |
688,15 |
726,024 |
-37,8739 |
|
4.58 |
689,85 |
592,652 |
97,1982 |
|
5.58 |
758,83 |
667,649 |
91,1811 |
|
6.58 |
813,63 |
822,538 |
-8,908 |
|
7.58 |
820,49 |
838,411 |
-17,9212 |
|
8.58 |
906,61 |
842,693 |
63,9171 |
|
9.58 |
902,04 |
1012,37 |
-110,332 |
|
10.58 |
941,57 |
982,419 |
-40,849 |
|
11.58 |
988,37 |
997,315 |
-8,94485 |
|
12.58 |
1024,29 |
1036,12 |
-11,8343 |
|
1.59 |
1117,68 |
1079,22 |
38,4592 |
|
2.59 |
1125,11 |
1169,65 |
-44,5403 |
|
3.59 |
1142,6 |
1174,87 |
-32,2675 |
|
4.59 |
1196,45 |
1182,38 |
14,0697 |
|
5.59 |
1193,84 |
1244,99 |
-51,1467 |
|
6.59 |
1163,26 |
1221,11 |
-57,8462 |
|
7.59 |
1141,02 |
1136,38 |
4,63982 |
|
8.59 |
1170,72 |
1118,97 |
51,7478 |
|
9.59 |
1132,32 |
1166,7 |
-34,3815 |
|
10.59 |
1143,91 |
1084,58 |
59,3268 |
|
11.59 |
1120,08 |
1114,61 |
5,47279 |
|
12.59 |
1128,26 |
1100,67 |
27,586 |
|
1.60 |
1207,35 |
1126,91 |
80,4352 |
|
2.60 |
1148,54 |
1227,18 |
-78,637 |
|
3.60 |
1163,89 |
1146,54 |
17,3461 |
|
4.60 |
1166,96 |
1168,97 |
-2,01088 |
|
5.60 |
1156,66 |
1188,62 |
-31,9586 |
|
6.60 |
1155,66 |
1164,36 |
-8,70498 |
|
7.60 |
1134,28 |
1125,4 |
8,87582 |
|
8.60 |
1104,87 |
1128,69 |
-23,8242 |
|
9.60 |
1055,55 |
1080,83 |
-25,2777 |
V |
|
|
Lower 95,0% |
Upper 95,0% |
Period |
Forecast |
Limit |
Limit |
10.60 |
1013,75 |
903,261 |
1124,25 |
ARIMA(4,4,1)
Forecasting - ConsGOODS
Data variable: ConsGOODS
Number of observations = 129
Start index = 1.50
Sampling interval = 1,0 month(s)
Forecast Summary
Nonseasonal differencing of order: 4
Forecast model selected: ARIMA(4,4,1)
Number of forecasts generated: 1
Number of periods withheld for validation: 1
|
Estimation |
Validation |
Statistic |
Period |
Period |
RMSE |
61,2656 |
10,1505 |
MAE |
46,3525 |
10,1505 |
MAPE |
4,84775 |
0,961634 |
ME |
1,45374 |
-10,1505 |
MPE |
0,181943 |
-0,961634 |
ARIMA Model Summary
Parameter |
Estimate |
Stnd. Error |
t |
P-value |
AR(1) |
-1,3335 |
0,07759 |
-17,1865 |
0,000000 |
AR(2) |
-1,19158 |
0,110172 |
-10,8156 |
0,000000 |
AR(3) |
-0,883211 |
0,10758 |
-8,20977 |
0,000000 |
AR(4) |
-0,478388 |
0,0802365 |
-5,96222 |
0,000000 |
MA(1) |
0,977607 |
0,0115877 |
84,3658 |
0,000000 |
Backforecasting: yes
Estimated white noise variance = 3814,48 with 120 degrees of freedom
Estimated white noise standard deviation = 61,7615
Number of iterations: 9
Forecast Table for ConsGOODS
Model: ARIMA(4,4,1)
V = withheld for validation
Period |
Data |
Forecast |
Residual |
|
1.50 |
813,17 |
|
|
|
2.50 |
877,02 |
|
|
|
3.50 |
844,36 |
|
|
|
4.50 |
856,69 |
|
|
|
5.50 |
924,97 |
845,132 |
79,8379 |
|
6.50 |
953,18 |
950,767 |
2,41256 |
|
7.50 |
892,74 |
974,068 |
-81,3277 |
|
8.50 |
874,46 |
840,333 |
34,1271 |
|
9.50 |
771,4 |
856,977 |
-85,5771 |
|
10.50 |
785,72 |
679,511 |
106,209 |
|
11.50 |
829,36 |
702,891 |
126,469 |
|
12.50 |
865,08 |
827,312 |
37,7681 |
|
1.51 |
892,15 |
929,409 |
-37,2586 |
|
2.51 |
947,28 |
935,91 |
11,3697 |
|
3.51 |
948,6 |
1056,59 |
-107,987 |
|
4.51 |
992,79 |
976,765 |
16,0251 |
|
5.51 |
1017,36 |
1013,53 |
3,82848 |
|
6.51 |
997,49 |
1042,39 |
-44,9044 |
|
7.51 |
911,97 |
990,719 |
-78,7492 |
|
8.51 |
837,21 |
822,04 |
15,1703 |
|
9.51 |
857,42 |
743,186 |
114,234 |
|
10.51 |
798,01 |
797,202 |
0,808137 |
|
11.51 |
859,33 |
731,469 |
127,861 |
|
12.51 |
849,27 |
871,541 |
-22,2712 |
|
1.52 |
838,65 |
898,911 |
-60,2608 |
|
2.52 |
824,31 |
866,887 |
-42,5768 |
|
3.52 |
820,56 |
797,322 |
23,2376 |
|
4.52 |
821,28 |
839,375 |
-18,0949 |
|
5.52 |
812,44 |
784,024 |
28,4164 |
|
6.52 |
786,55 |
807,083 |
-20,5333 |
|
7.52 |
804,84 |
766,584 |
38,2557 |
|
8.52 |
834,95 |
808,47 |
26,4803 |
|
9.52 |
863,61 |
859,557 |
4,05253 |
|
10.52 |
816,88 |
895,829 |
-78,9485 |
|
11.52 |
862,39 |
805,942 |
56,4484 |
|
12.52 |
839,67 |
890,657 |
-50,9873 |
|
1.53 |
812,22 |
832,219 |
-19,999 |
|
2.53 |
822,04 |
771,051 |
50,9894 |
|
3.53 |
823,26 |
797,292 |
25,9676 |
|
4.53 |
843,39 |
846,564 |
-3,17364 |
|
5.53 |
865,42 |
831,739 |
33,6811 |
|
6.53 |
825,66 |
899,236 |
-73,5756 |
|
7.53 |
850,26 |
824,871 |
25,3894 |
|
8.53 |
828,34 |
847,237 |
-18,8971 |
|
9.53 |
783,02 |
819,89 |
-36,8702 |
|
10.53 |
807,71 |
731,878 |
75,8323 |
|
11.53 |
791,73 |
786,813 |
4,91681 |
|
12.53 |
829,32 |
803,033 |
26,287 |
|
1.54 |
863,65 |
832,765 |
30,8847 |
|
2.54 |
878,19 |
911,599 |
-33,4091 |
|
3.54 |
894,68 |
931,989 |
-37,3092 |
|
4.54 |
873,43 |
907,676 |
-34,2456 |
|
5.54 |
841,42 |
881,221 |
-39,8005 |
|
6.54 |
923,94 |
795,754 |
128,186 |
|
7.54 |
919,01 |
946,374 |
-27,3636 |
|
8.54 |
919,19 |
941,175 |
-21,9845 |
|
9.54 |
881,18 |
917,009 |
-35,8286 |
|
10.54 |
911,06 |
868,926 |
42,1337 |
|
11.54 |
921,6 |
932,831 |
-11,2306 |
|
12.54 |
1016,39 |
895,418 |
120,972 |
|
1.55 |
1055,37 |
1089,7 |
-34,3328 |
|
2.55 |
1103,51 |
1128,85 |
-25,336 |
|
3.55 |
1112,47 |
1191,41 |
-78,9421 |
|
4.55 |
1119,03 |
1141,78 |
-22,7523 |
|
5.55 |
1113,04 |
1139,2 |
-26,1576 |
|
6.55 |
1028,2 |
1073,07 |
-44,8686 |
|
7.55 |
1038,78 |
951,898 |
86,8823 |
|
8.55 |
1086,43 |
980,949 |
105,481 |
|
9.55 |
1105,96 |
1105,27 |
0,694917 |
|
10.55 |
1125,8 |
1132,19 |
-6,3939 |
|
11.55 |
1124,88 |
1154,31 |
-29,4257 |
|
12.55 |
1162,68 |
1182,67 |
-19,9932 |
|
1.56 |
1204,92 |
1190,38 |
14,5387 |
|
2.56 |
1232,24 |
1231,09 |
1,1536 |
|
3.56 |
1138,69 |
1268,52 |
-129,826 |
|
4.56 |
1230,79 |
1087,2 |
143,586 |
|
5.56 |
1271,72 |
1259,52 |
12,2038 |
|
6.56 |
1307,78 |
1315,12 |
-7,34223 |
|
7.56 |
1328,18 |
1339,46 |
-11,285 |
|
8.56 |
1310,47 |
1354,5 |
-44,0255 |
|
9.56 |
1326,15 |
1368,69 |
-42,538 |
|
10.56 |
1344,56 |
1291,9 |
52,6616 |
|
11.56 |
1348,83 |
1345,45 |
3,38147 |
|
12.56 |
1324,74 |
1344,73 |
-19,9872 |
|
1.57 |
1347,72 |
1302,93 |
44,7917 |
|
2.57 |
1213,49 |
1363,4 |
-149,908 |
|
3.57 |
1145,62 |
1121,55 |
24,0684 |
|
4.57 |
1180,98 |
1026,46 |
154,518 |
|
5.57 |
1181,07 |
1148,69 |
32,3848 |
|
6.57 |
1145,27 |
1187,98 |
-42,7116 |
|
7.57 |
995,52 |
1100,04 |
-104,517 |
|
8.57 |
957,73 |
939,111 |
18,6188 |
|
9.57 |
1030,47 |
888,658 |
141,812 |
|
10.57 |
987,7 |
1017,06 |
-29,3633 |
|
11.57 |
874,21 |
971,073 |
-96,8627 |
|
12.57 |
749,78 |
791,346 |
-41,5661 |
|
1.58 |
815,25 |
679,256 |
135,994 |
|
2.58 |
788,89 |
800,797 |
-11,907 |
|
3.58 |
688,15 |
733,232 |
-45,0816 |
|
4.58 |
689,85 |
618,859 |
70,9913 |
|
5.58 |
758,83 |
691,122 |
67,7076 |
|
6.58 |
813,63 |
853,129 |
-39,4985 |
|
7.58 |
820,49 |
841,854 |
-21,3642 |
|
8.58 |
906,61 |
869,08 |
37,5298 |
|
9.58 |
902,04 |
1033,32 |
-131,284 |
|
10.58 |
941,57 |
949,647 |
-8,07697 |
|
11.58 |
988,37 |
950,612 |
37,7577 |
|
12.58 |
1024,29 |
1019,88 |
4,41367 |
|
1.59 |
1117,68 |
1079,46 |
38,2228 |
|
2.59 |
1125,11 |
1167,71 |
-42,5996 |
|
3.59 |
1142,6 |
1189,74 |
-47,135 |
|
4.59 |
1196,45 |
1159,96 |
36,4884 |
|
5.59 |
1193,84 |
1230,6 |
-36,7628 |
|
6.59 |
1163,26 |
1209,64 |
-46,3808 |
|
7.59 |
1141,02 |
1105,74 |
35,2763 |
|
8.59 |
1170,72 |
1112,53 |
58,1933 |
|
9.59 |
1132,32 |
1169,87 |
-37,5538 |
|
10.59 |
1143,91 |
1087,08 |
56,83 |
|
11.59 |
1120,08 |
1135,29 |
-15,2067 |
|
12.59 |
1128,26 |
1118,94 |
9,31604 |
|
1.60 |
1207,35 |
1133,41 |
73,9389 |
|
2.60 |
1148,54 |
1245,71 |
-97,1657 |
|
3.60 |
1163,89 |
1164,69 |
-0,798418 |
|
4.60 |
1166,96 |
1152,26 |
14,7021 |
|
5.60 |
1156,66 |
1185,92 |
-29,2558 |
|
6.60 |
1155,66 |
1149,16 |
6,50303 |
|
7.60 |
1134,28 |
1109,19 |
25,0931 |
|
8.60 |
1104,87 |
1147,22 |
-42,3523 |
|
9.60 |
1055,55 |
1065,7 |
-10,1505 |
V |
|
|
Lower 95,0% |
Upper 95,0% |
Period |
Forecast |
Limit |
Limit |
10.60 |
1001,46 |
879,178 |
1123,75 |
